Question

A person travels along a straight road for half the distance with velocity v1 and remaining half distance with velocity v2 the average velocity is given by

Answer 1

Let Let T be the time taken by the person to cover complete distance.

Case I:
let x1 be the half distance covered.
speed=v1
time taken to cover the  first  half of the journey :
t1=distance/speed
=(x/2)/v1

Case II
let x2 be the half distance covered.
speed=v2
time taken to cover the  second half of the journey :
t2=distance/speed
=(x/2)/v2

Total time=T=t1+t2
=x/(2v1)+x/(2v2)

T=x/2[1/v1+1/v2]

=x[v1+v2]/2v1v2

Average Velocity= Displacement/ total time
=x/x[v1+v2]/2v1v2
=2v1v2/(v1+v2)

∴Average velocity is given by 2v1v2/(v1+v2)

Answer 2

Explanation:

Avg Velocity =

total displacement /total time interval

Lets consider x is half covered distance

T1=first half distance time

T2 = next half distance .....

X+X= total displacement

T1+T2 = total time interval

Where T1= X /V1 ( :.speed =distance/time)

T2= X /V2

= total dispacement = 2x

= total time interval = X/v1 + X/v2

By putting the values in Avg velocity formulae

= 2v1v2/v1+v2 (ans)

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